Hello! Can you provide response to each part of the problem by using physics concepts or formulas? Please also provide all math/formula/conceptual steps so that I can check my own work. This question may involve Center of Mass, Centrifugal Force, Moment of Inertia, Kinetic Energy, Uniform Circle, Potential Energy, Torque, Conservation of Mechanical Energy, or other Physics concepts.

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Physics Practice Problem: Resisting rollover If a vehicle tries to turn around a corner too quickly, it can rollover onto its side (or worse). Here we analyze the conditions of stability for a bicycle and a car. (a) (C) A bicycle and its rider have a combined center of mass a height in above the ground and a total mass m. The bike. is moving at a constant speed 1! in a circle of radius 1'. You know from experience that. you need to lean into a turn so that the bike makes an angle 9 with respect to the vertical. What lean angle should the bike. make so that the bike. doesn't rollover or fall to the. ground? Assume the coefcient of friction between the tires and the. road is strong enough to prevent slipping. Assume that gravity acts solely on the center of mass. which is located a height I: off the. ground when in the upright position. Hint: using the. apparent. centrifugal force in an accelerating reference frame may be helpful to solve this problem. but it is not necessary. A four-wheeled vehicle. is more. stable than a bike. but it can still topple over if it corners a turn too sharply. The car has a center of mass a height it off the ground and a width between the centerline of two wheels on the. same axle (called "track") of in. What is the maximum speed the car can go around a turn of radius 1' without rolling over? Again. assume the. coefcient of static friction is great enough to prevent slipping. A friend tells you to add weight to the roof rack of an SUV to make the. vehicle heavier to prevent rolling over. Would this work? Explain why or why not